using Newtonsoft.Json;
using Newtonsoft.Json.Serialization;
using Utils.Helpers;
namespace YourNamespace
{
    public static class JsonSerializationExtensions
    {
        private static readonly SnakeCaseNamingStrategy _snakeCaseNamingStrategy
            = new SnakeCaseNamingStrategy();
        private static readonly JsonSerializerSettings _snakeCaseSettings = new JsonSerializerSettings
        {
            ContractResolver = new DefaultContractResolver
            {
                NamingStrategy = _snakeCaseNamingStrategy
            }
        };
        public static string ToSnakeCase(this T instance)
        {
            if (instance == null)
              {
                   throw new ArgumentNullException(paramName: nameof(instance));
               }
            return JsonConvert.SerializeObject(instance, _snakeCaseSettings);
        }
        public static string ToSnakeCase(this string @string)
        {
            if (@string == null)
              {
                   throw new ArgumentNullException(paramName: nameof(@string));
               }
            return _snakeCaseNamingStrategy.GetPropertyName(@string, false);
        }
    }
}

using System.Text.Json;
using Utils.Serialization;
namespace YourNamespace
{
    public class SnakeCaseNamingPolicy : JsonNamingPolicy
    {
        public override string ConvertName(string name) => name.ToSnakeCase();
    }
}

public class Startup
{
  public void ConfigureServices(IServiceCollection services)
  {
    // ...
    services
        .AddMvc()
        .AddJsonOptions(x =>
        {
            x.JsonSerializerOptions.PropertyNamingPolicy = new SnakeCaseNamingPolicy();
        });
    // ...
  }
}

using System;
using System.Collections.Generic;
using System.Net;
using Microsoft.AspNetCore.Mvc;
namespace YourNamespace
{
    public class ValidationProblemDetails : ProblemDetails
    {
        // 400 status ccode is usually used for input validation errors
        public const int ValidationStatusCode = (int)HttpStatusCode.BadRequest;
        public ValidationProblemDetails(ICollection validationErrors)
        {
            ValidationErrors = validationErrors;
            Status = ValidationStatusCode;
            Title = "Request Validation Error";
        }
        public ICollection ValidationErrors { get; }
        public string RequestId => Guid.NewGuid().ToString();
    }
}

using System.Collections.Generic;
using System.Linq;
using System.Threading.Tasks;
using Microsoft.AspNetCore.Mvc;
using Utils.Serialization;
namespace YourNamespace
{
    public class ValidationProblemDetailsResult : IActionResult
    {
        public async Task ExecuteResultAsync(ActionContext context)
        {
            var modelStateEntries = context.ModelState
                .Where(e => e.Value.Errors.Count > 0)
                .ToArray();
            var errors = new List();
            if (modelStateEntries.Any())
            {
                foreach (var (key, value) in modelStateEntries)
                {
                    errors.AddRange(value.Errors
                        .Select(modelStateError => new ValidationError(
                            name: key.ToSnakeCase(),
                            description: modelStateError.ErrorMessage)));
                }
            }
            await new JsonErrorResponse(
                context: context.HttpContext,
                error: new ValidationProblemDetails(errors),
                statusCode: ValidationProblemDetails.ValidationStatusCode).WriteAsync();
        }
    }
}

public class Startup
{
   // ...
  public void ConfigureServices(IServiceCollection services)
  {
    // ...
    services
        .Configure(x =>
        {
            x.InvalidModelStateResponseFactory = ctx => new ValidationProblemDetailsResult();
        });
    // ...
  }
}